Yesterday, the authorities said they had no suspects in Mr. Oliver's killing, which took place about 4 p.m. in the Vale of Cashmere, a lush, hilly swath near Grand Army Plaza, which draws bird-watchers and, in good weather, gay men looking for sexual encounters.

Reared in rural Virginia, one of seven children born to a tobacco-farming couple, Mr. Oliver was a quiet, courtly man who, according to family members, held a variety of jobs after moving to New York in the 1970's: as a worker in a handbag factory, a salesman at a jewelry store and, in recent years, a housecleaner for affluent clients in Manhattan.

Wilson Oliver, 67, said he could not imagine why anyone would want to harm his brother, a pacific soul who mostly kept to himself.

Although he worked when he could, his brother said, William Oliver did not earn enough money to rent his own place so he alternated between his older brother's apartment in Bedford-Stuyvesant and his sister's house in Flatbush. Mr. Oliver would get a bed and home-cooked meals, and his siblings would enjoy his good-natured company and the benefits of his industriousness.

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In the winter, Mr. Oliver shoveled snow, and in the spring, he prepared his sister's backyard vegetable garden. Not long ago, he painted her living room robin's-egg blue.

"You didn't have to ask him to do anything," said the sister, Shirley Puryear, 69. "He just did it."

Walking and listening to music, family members said, seemed to be his solace. He would regularly stroll the 3 1/2 miles between his brother's and sister's homes. Sometimes, he would hike all the way into Manhattan. "He'd just walk and walk and walk," said a niece, Evelyn Puryear.

Prospect Park is near the route he usually took between the homes of his brother and his sister. Last night, investigators said they were exploring whether Mr. Oliver was the victim of a robbery, a random act of brutality or perhaps an attack motivated by homophobia. When asked, Mr. Oliver's brother and sister said they did not know whether he was gay.

Over the years, the Vale of Cashmere has often been the site of attacks on gay men. Last October, two men were shot and wounded there; in 2000, a man dressed as a ninja slashed and beat five men there. No arrests were made in those attacks.

Clarence Patton, executive director of the New York City Gay and Lesbian Anti-Violence Project, said he was consulted yesterday by an investigator from the Police Department's hate crimes unit, who was trying to determine whether the victim was gay.

Though Mr. Patton said he did not know, he said at least 10 percent of victims of anti-gay violence are not gay, but rather are targeted in places thought to be gathering spots for gay men or lesbians. "It's hard to say whether you hope it was a robbery or an anti-gay attack," he said. "At the end of the day, a man is dead, and it doesn't really matter."